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@benchmark fobj($pinit)

# Now we benchmark the gradient
@benchmark gfobj($pinit)</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Chael A, et al. <em>Inteferometric Imaging Directly with Closure Phases</em> 2018 ApJ 857 1 arXiv:1803/07088</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../vlbi_imaging_problem/">Introduction to the VLBI Imaging Problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 9 August 2023 17:15">Wednesday 9 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
@benchmark gfobj($pinit)</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Chael A, et al. <em>Inteferometric Imaging Directly with Closure Phases</em> 2018 ApJ 857 1 arXiv:1803/07088</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../vlbi_imaging_problem/">Introduction to the VLBI Imaging Problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Thursday 10 August 2023 17:45">Thursday 10 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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\begin{pmatrix}
\tilde{I} + \tilde{Q} &amp; \tilde{U} + i\tilde{V}\\
\tilde{U} - i\tilde{V} &amp; \tilde{I} - \tilde{Q}
\end{pmatrix}.\]</p><p>where e.g., <span>$\left&lt;XY^*\right&gt; = 2\left&lt;v_{pX}v^*_{pY}\right&gt;$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../vlbi_imaging_problem/">« Introduction to the VLBI Imaging Problem</a><a class="docs-footer-nextpage" href="../examples/data/">Loading Data into Comrade »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 9 August 2023 17:15">Wednesday 9 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{pmatrix}.\]</p><p>where e.g., <span>$\left&lt;XY^*\right&gt; = 2\left&lt;v_{pX}v^*_{pY}\right&gt;$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../vlbi_imaging_problem/">« Introduction to the VLBI Imaging Problem</a><a class="docs-footer-nextpage" href="../examples/data/">Loading Data into Comrade »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Thursday 10 August 2023 17:45">Thursday 10 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Model Interface · Comrade.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Comrade.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../benchmarks/">Benchmarks</a></li><li><a class="tocitem" href="../vlbi_imaging_problem/">Introduction to the VLBI Imaging Problem</a></li><li><a class="tocitem" href="../conventions/">Conventions</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../examples/data/">Loading Data into Comrade</a></li><li><a class="tocitem" href="../examples/geometric_modeling/">Geometric Modeling of EHT Data</a></li><li><a class="tocitem" href="../examples/imaging_closures/">Imaging a Black Hole using only Closure Quantities</a></li><li><a class="tocitem" href="../examples/imaging_vis/">Stokes I Simultaneous Image and Instrument Modeling</a></li><li><a class="tocitem" href="../examples/imaging_pol/">Polarized Image and Instrumental Modeling</a></li><li><a class="tocitem" href="../examples/hybrid_imaging/">Hybrid Imaging of a Black Hole</a></li></ul></li><li><span class="tocitem">Libraries</span><ul><li><a class="tocitem" href="../libs/optimization/">ComradeOptimization</a></li><li><a class="tocitem" href="../libs/ahmc/">ComradeAHMC</a></li><li><a class="tocitem" href="../libs/nested/">ComradeNested</a></li><li><a class="tocitem" href="../libs/dynesty/">ComradeDynesty</a></li><li><a class="tocitem" href="../libs/adaptmcmc/">ComradeAdaptMCMC</a></li></ul></li><li><a class="tocitem" href="../base_api/">ComradeBase API</a></li><li><a class="tocitem" href="../api/">Comrade API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Model Interface</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Model Interface</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/ptiede/Comrade.jl/blob/main/docs/src/interface.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Model-Interface"><a class="docs-heading-anchor" href="#Model-Interface">Model Interface</a><a id="Model-Interface-1"></a><a class="docs-heading-anchor-permalink" href="#Model-Interface" title="Permalink"></a></h1><p>For the interface for sky models please see <a href="https://github.com/EHTJulia/VLBISkyModels.jl"><code>VLBISkyModels</code></a>.</p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 9 August 2023 17:15">Wednesday 9 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Model Interface · Comrade.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">Comrade.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../benchmarks/">Benchmarks</a></li><li><a class="tocitem" href="../vlbi_imaging_problem/">Introduction to the VLBI Imaging Problem</a></li><li><a class="tocitem" href="../conventions/">Conventions</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../examples/data/">Loading Data into Comrade</a></li><li><a class="tocitem" href="../examples/geometric_modeling/">Geometric Modeling of EHT Data</a></li><li><a class="tocitem" href="../examples/imaging_closures/">Imaging a Black Hole using only Closure Quantities</a></li><li><a class="tocitem" href="../examples/imaging_vis/">Stokes I Simultaneous Image and Instrument Modeling</a></li><li><a class="tocitem" href="../examples/imaging_pol/">Polarized Image and Instrumental Modeling</a></li><li><a class="tocitem" href="../examples/hybrid_imaging/">Hybrid Imaging of a Black Hole</a></li></ul></li><li><span class="tocitem">Libraries</span><ul><li><a class="tocitem" href="../libs/optimization/">ComradeOptimization</a></li><li><a class="tocitem" href="../libs/ahmc/">ComradeAHMC</a></li><li><a class="tocitem" href="../libs/nested/">ComradeNested</a></li><li><a class="tocitem" href="../libs/dynesty/">ComradeDynesty</a></li><li><a class="tocitem" href="../libs/adaptmcmc/">ComradeAdaptMCMC</a></li></ul></li><li><a class="tocitem" href="../base_api/">ComradeBase API</a></li><li><a class="tocitem" href="../api/">Comrade API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Model Interface</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Model Interface</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/ptiede/Comrade.jl/blob/main/docs/src/interface.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Model-Interface"><a class="docs-heading-anchor" href="#Model-Interface">Model Interface</a><a id="Model-Interface-1"></a><a class="docs-heading-anchor-permalink" href="#Model-Interface" title="Permalink"></a></h1><p>For the interface for sky models please see <a href="https://github.com/EHTJulia/VLBISkyModels.jl"><code>VLBISkyModels</code></a>.</p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Thursday 10 August 2023 17:45">Thursday 10 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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